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TRS Standard pair #516960970
details
property
value
status
complete
benchmark
thiemann35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.82294201851 seconds
cpu usage
7.738448718
max memory
5.53517056E8
stage attributes
key
value
output-size
21274
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 20 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) ATransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) ATransformationProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) QDPApplicativeOrderProof [EQUIVALENT, 50 ms] (27) QDP (28) UsableRulesProof [EQUIVALENT, 0 ms] (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) The set Q consists of the following terms: a(a(append, nil), x0)
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